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Show that the points A(3, 0), B(4, 5), C(-1, 4) and D(-2, -1) are the vertices of a rhombus. Find its area.

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The correct Answer is:
24 sq units
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RS AGGARWAL-COORDINATE GEOMETRY-Exercise 6A
  1. If the point C(-2, 3) is equidistant from the points A(3, -1) and B(x,...

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  2. If the point P(2, 2) is equidistant from the points A(-2, k) and B(-2k...

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  3. (i) If the point (x, y) is equidistant from the points (a+b, b-a) and ...

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  4. Using the distance formula, show that the given points are collinear. ...

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  5. Show that the points A(7, 10), B(-2, 5) and C(3, -4) are the vertices ...

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  6. Show that the points A(3, 0), B(6, 4) and C(-1, 3) are the vertices of...

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  7. If A(5, 2), B(2, -2) and C(-2, t) are the vertices of a right triangle...

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  8. Prove that the points A(2, 4), B(2, 6) and C(2 + sqrt(3), 5) are the v...

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  9. Show that the points (-3, -3), (3, 3) and (-3sqrt(3), 3sqrt(3)) are th...

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  10. The points A(-5, 6), B(3, 0) and C(9, 8) are the vertices of an isosce...

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  11. Show that the points O(0, 0), A(3, sqrt(3)) "and "B(3, -sqrt(3)) are t...

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  12. Show that the following points are the vertices of a square: (i) A(...

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  13. Show that the points A(-3, 2), B(-5, -5), C(2, -3) and D(4, 4) are the...

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  14. Show that the points A(3, 0), B(4, 5), C(-1, 4) and D(-2, -1) are the ...

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  15. Show that the points A(6, 1), B(8, 2), C(9, 4) and D(7, 3) are the ver...

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  16. Show that the points A(2, 1), B(5, 2), C(6, 4) and D(3, 3) are the ang...

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  17. Show that A(1, 2), B(4, 3), C(6, 6) and D(3, 5) are the vertices of a ...

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  18. Show that the following points are the vertices of a rectangle. (i)...

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  19. Show that Delta ABC with vertices A(-2, 0), B(0, 2) and C(2, 0) is sim...

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  20. Show that Delta ABC, where A(-2, 0), B(2, 0), C(0,2) and DeltaPQR whe...

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